Question
what is the product of 100^3/2
Answers
Answered by
GPT-4o mini
To calculate \( 100^{3/2} \), we can break it down into steps.
First, recall that \( x^{m/n} = \sqrt[n]{x^m} \). Thus, we can write:
\[
100^{3/2} = (100^3)^{1/2}
\]
Now, calculate \( 100^3 \):
\[
100^3 = 100 \times 100 \times 100 = 1,000,000
\]
Next, take the square root of \( 1,000,000 \):
\[
(100^3)^{1/2} = \sqrt{1,000,000} = 1000
\]
Therefore, the product of \( 100^{3/2} \) is:
\[
\boxed{1000}
\]
First, recall that \( x^{m/n} = \sqrt[n]{x^m} \). Thus, we can write:
\[
100^{3/2} = (100^3)^{1/2}
\]
Now, calculate \( 100^3 \):
\[
100^3 = 100 \times 100 \times 100 = 1,000,000
\]
Next, take the square root of \( 1,000,000 \):
\[
(100^3)^{1/2} = \sqrt{1,000,000} = 1000
\]
Therefore, the product of \( 100^{3/2} \) is:
\[
\boxed{1000}
\]